Download Algebra 1A1/1A2 Sample Assessment Items

Los Angeles Unified School District
Algebra 1A1/1A2
Sample Assessment Items
The purpose of these sample assessment items is to provide teachers with examples of questions that address
the assessed standards. Although the assessment items will not be identical to these samples, the test format,
level of rigor, and type of questions will be similar. Not all assessed standards are represented. The intent is
not to create a pretest or to layer an additional assessment
MULTIPLE CHOICE QUESTIONS
Sample Item #1
Algebra I
1.0 Students identify and use the arithmetic properties of subsets of
integers and rational, irrational, and real numbers, including closure
properties for the four basic arithmetic operations where applicable.
Strand:
*Standard:
Four arithmetic statements are shown in the box below.
5+2=7
5−2 =3
5 × 2 = 10
5÷2=2
1
2
These four statements show that closure for integers applies to all operations except
A addition.
B division.
C subtraction.
D multiplication.
Answer: B
*assessed standard
key standard
Los Angeles Unified School District
Algebra 1A1/1A2
Sample Assessment Items
Sample Item #2
Strand:
Algebra I
4.0 Students simplify expressions before solving linear equations and
inequalities in one variable, such as 3 ( 2 x + 5) + 4 ( x − 2 ) = 12 .
*Standard:
Which of the following equations is equivalent to x−
1
1
(2 − x) = ( x+2)?
2
2
1
x +1
2
A
−1=
B
1
1
1 x −1= x +1
2
2
C
2x − 1 =
1
x +1
2
D
2x + 1 =
1
x +1
2
Answer: B
Sample Item #3
Strand:
*Standard:
Algebra I
5.0
Students solve multi-step problems, including word problems,
involving linear equations and linear inequalities in one variable and
provide justification for each step.
Daria has a grocery budget of $50 per week. She spent $63.92 on groceries this week, but plans to
spend less for the next 3 weeks to stay within her budget. What is the average amount that Daria
should spend on groceries per week for the next three weeks to meet this goal?
A
B
C
D
$34.02
$36.08
$45.36
$46.52
*assessed standard
key standard
Los Angeles Unified School District
Algebra 1A1/1A2
Sample Assessment Items
Sample Item #4
Strand:
*Standard:
Algebra I
6.0
Students graph a linear equation, and compute the x- and y-intercepts.
If a line has a slope of 3 and an x–intercept of − 2, what is the y–intercept?
A −6
B −2
C 1
D 6
Answer: D
Sample Item #5
Strand:
Standard:
Algebra 1
5.0 Students solve multistep problems, including word problems, involving linear
equations and linear inequalities in one variable and provide justification for
each step.
A prize of $25,000 is to be divided among Fernando, Kathy, and Joel. Fernando is to receive $5,000
more than Kathy, and Kathy is to receive twice as much as Joel. How much should Joel receive?
A
B
C
D
$4,000
$6,700
$8,000
$13,000
Answer: A
*assessed standard
key standard
Los Angeles Unified School District
Algebra 1A1/1A2
Sample Assessment Items
Sample Item #6
Strand:
*Standard:
Algebra I
9.0
Students solve a system of two linear equations in two variables
algebraically, and are able to interpret the answer graphically.
Students are able to solve a system of two linear inequalities in two
variables, and to sketch the solution sets.
Which of the following systems of linear inequalities is shown in the graph below?
A
B
C
D
y < 3 and y > x + 1
y > 3 and y < x + 1
y > 3 and y > x + 1
y < 3 and y < x + 1
Answer: B
Sample Item #7
Strand:
*Standard:
Algebra I
5.0 Students solve multi-step problems, including word problems,
involving linear equations and linear inequalities in one variable and
provide justification for each step.
If 2 x + 6 = 20, what is the value of − 3 x + 5?
A −54
B −36
C −34
D −16
Answer: D
*assessed standard
key standard
Los Angeles Unified School District
Algebra 1A1/1A2
Sample Assessment Items
Sample Item #8
Strand:
*Standard:
Algebra I
6.0
Students graph a linear equation, and compute the x- and yintercepts (e.g., graph 2x + 6y = 4). They are also able to sketch the
region defined by linear inequality (e.g., they sketch the region
defined by 2x + 6y < 4).
Which is the graph of y < 3 x + 2 ?
Answer: B
CONSTRUCTED RESPONSE
Strand:
Algebra I
*Standard:
2.0
For the equation y = 1 −
•
•
Students understand and use such operations as taking the opposite,
finding the reciprocal.
1
, write the following:
x
the opposite of y
the reciprocal of y
For both the opposite and the reciprocal, show each step of the operation that proves your answers
are correct.
*assessed standard
key standard
Los Angeles Unified School District
Algebra 1A1/1A2
Sample Assessment Items
Rubric:
4-point response: The student indicates an advanced proficiency of taking the opposite and finding the
reciprocal.
1
• The student correctly writes the opposite of y as −1.
x
x
.
• The student correctly writes the reciprocal of y as
x −1
• The student proves that the answer is the opposite by showing the sum of the two is zero.

1 1
1 1
y + (− y )= 1 − +  − 1 = 1 − 1 + − = 0

x  x
x x
• The student proves that the second answer is the reciprocal by showing the product of the two is
one.
1 
1   x 
x
x − 1 x ( x − 1)
 =
i
y   = 1 −  i 
=
=1
 y  

x   x − 1  x − 1
x
( x − 1) x
3-point response: The student indicates proficiency of taking the opposite and finding the reciprocal.
•
The student correctly finds the opposite and reciprocal of y and attempts to prove both are true
but makes a mistake on one of the proofs.
2-point response: The student indicates partial proficiency of taking the opposite and finding the
reciprocal.
•
The student correctly finds the opposite and reciprocal of y and attempts to prove both are true
but is unable to do so.
OR
•
The student does not find either or both the opposite and reciprocal correctly but does show some
good work strategies and attempts the proofs.
1-point response: The student indicates little or no proficiency of taking the opposite and finding the
reciprocal.
•
•
The student attempts the problem but does no part correctly.
OR
The student does not attempt the problem.
*assessed standard
key standard
LOS ANGELES UNIFIED SCHOOL DISTRICT
Instructional Support Services
District Mathematics Program
Algebra 1A1/1A2
BLUEPRINT: 2004-05 Quarter 1
Multiple
Choice
STANDARD
1.0
Students identify and use the arithmetic properties of subsets
of integers and rational, irrational, and real numbers,
including closure properties for the four basic operations
where applicable.
6
2.0
Students understand and use such operations as taking the
opposite, finding the reciprocal, taking a root, and raising to
a fractional power. They understand and use the rules of
exponents.
12
4.0
Students simplify expressions before solving linear equations
and inequalities in one variable.
12
TOTAL
30
Key standard
Constructed
Response
1
1
LOS ANGELES UNIFIED SCHOOL DISTRICT
Instructional Support Services
District Mathematics Program
Algebra 1A1/1A2
BLUEPRINT: 2004-05 Quarter 2
STANDARD
Multiple
Choice
Constructed
Response
1
5.0
Students solve multi-step problems, including word
problems, involving linear equations in one variable and
provide justification for each step.
9
6.0
Students graph a linear equation and compute the x- and yintercepts (e.g., graph 2x+y = 4). They are also able to
sketch the region defined by linear inequality (e.g., they
sketch the region defined by 2x + 6y < 4)
10
7.0
Students verify that a point lies on a line, given an equation
of the line. Students are able to derive linear equations using
the point-slope formula.
9
Key standard
Linking Items from Quarter 1
2
TOTAL
30
1
LOS ANGELES UNIFIED SCHOOL DISTRICT
Instructional Support Services
District Mathematics Program
Algebra 1A1/1A2
BLUEPRINT: 2004-05 Quarter 3
Multiple
Choice
STANDARD
3.0
Students solve equations and inequalities involving absolute
values.
3
5.0
Students solve multi-step problems, including word
problems, involving linear equations and linear inequalities
in one variable and provide justification for each step.
7
6.0
Students graph a linear equation and compute the x- and yintercepts (e.g., graph 2x + 6y = 4). They are also able to
sketch the region defined by linear inequality (e.g., sketch
the region defined by 2x + 6y < 4).
5
7.0
Students verify that a point lies on a line, given the equation
of the line. Students are able to derive the equation of a line
by using the point-slope formula.
6
9.0
Students solve a system of two linear equations in two
variables algebraically and are able to interpret the answer
graphically. Students are able to solve a system of two linear
inequalities in two variables and to sketch the solution sets.
7
Linking Items from Quarter 2
2
TOTAL
30
Key standard
Constructed
Response
1
1
LOS ANGELES UNIFIED SCHOOL DISTRICT
Instructional Support Services
District Mathematics Program
Algebra 1A1 (End-of-Course)
BLUEPRINT: 2004-05 Quarter 4
STANDARD
Multiple
Choice
4
Constructed
Response
2.0
Students understand and use such operations as taking the
opposite, finding the reciprocal, taking a root, and raising to a
fractional power. They understand and use the rules of
exponents.
3.0
Students solve equations and inequalities involving absolute
values.
4
4.0
Students simplify expressions prior to solving linear equations
and inequalities in one variable, such as 3(2x-5)+4(x-2)=12
4
5.0
Students solve multistep problems, including word problems,
involving linear equations and linear inequalities in one variable
and provide justification for each step.
10
6.0
Students graph a linear equation and compute the x- and yintercepts (e.g., graph 2x+y = 4). They are also able to sketch
the region defined by linear inequality (e.g., they sketch the
region defined by 2x + 6y < 4)
10
7.0
Students verify that a point lies on a line, given an equation of
the line. Students are able to derive linear equations using the
point-slope formula.
10
8.0
Students understand the concept of parallel lines and
perpendicular lines and how those slopes are related. Students
are able to find the equation of a line perpendicular to a given
line that passes through a given point.
4
9.0
Students solve a system of two linear equations in two variables
algebraically and are able to interpret the answer graphically.
Students are able to solve a system of two linear inequalities in
two variables and to sketch the solution sets.
10
15.0
Students apply algebraic techniques to solve rate problems, work
problems, and percent mixture problems.
4
1
TOTAL
60
1
Key standard